Let S be the set of positive integers n for which
2 expresso shots + 1000 chemistry problems + n biology tests = n all-nighters
then 1 ϵ S since
2 expresso shots + 1000 chemistry problems + 1 biology test = 1 all-nighter
Assume k ϵ S
Then
2 expresso shots + 1000 chemistry problems + k biology tests = k all-nighters
Consider k+1 ϵ S
2 expresso shots + 1000 chemistry problems + k+1 biology tests = k+1 all-nighters
Thus k+1 ϵ S and Linh is still lost?